Device and method for editing a virtual, three-dimensional dental model by means of a virtual tool

ABSTRACT

The invention concerns a device ( 1 ) for editing a virtual 3-D model ( 2 ) of teeth ( 2.1, 2.2, 2.3, 2.4 ) positioned in a dental arch ( 9, 11 ) by means of a virtual tool ( 21, 22, 23, 24, 25, 26, 27, 28, 50 ). The tool ( 21, 22, 23, 24, 25, 26, 27, 28, 50 ) can be used on a first tooth ( 2.1, 2.3 ) of the 3-D model ( 2 ), whereby the corresponding application is carried out on a second mirrored tooth ( 2.2, 2.4 ), contralateral to the first tooth with respect to a plane of symmetry ( 12 ), that is, on the tooth on the other side of the plane of symmetry ( 12 ), which is positioned as a mirror image of the first tooth ( 2.1, 2.3 ) with respect to the plane of symmetry ( 12 ).

FIELD OF THE INVENTION

The invention concerns a device for editing a virtual 3-D model of teethpositioned in a dental arch by means of a virtual tool, together with acorresponding process for editing a virtual 3-D model.

PRIOR ART

Methods for the construction of a 3-D model of a dental arch are knownfrom the prior art, whereby the dental surfaces are incorporated or asurface is created artificially using the wax-up method prior to thepreparation and is virtually transferred onto the surface of the 3-Dmodel. Partly for this reason, the three-dimensional data of the dentalsurface are copied.

In the manual creation of a restoration by the dental technician, thedental technician tries to mold the dental surface of the restorationsuch that it corresponds with the dental surface of the contralateraltooth, while taking the morphology of the natural dentition intoaccount. Structuring the restoration in precise symmetry with thecontralateral tooth, however, is seldom achieved.

Particularly in a restoration in the anterior tooth region, the symmetryof the restoration is a crucial factor for an esthetic restoration. Thesymmetry has reference to a plane of symmetry, which corresponds to thecentral facial axis and which is positioned between quadrants 1 and 2 orbetween quadrants 3 and 4. In the virtual planning of the restorationusing CAD tools, the changes made by the user must also be performedmirror-symmetrically on the contralateral tooth in order to ensure thesymmetry. This requires a high level of skill in the application of theCAD tools and an esthetic perception on the part of the user.

A method for the construction of the surface of a tooth replacementconsisting of three-dimensional data is known from DE 10 2004 938 136A1, whereby the three-dimensional data of a dental surface of a storedtooth are used at least as part of the surface of the tooth replacementto be fabricated. For this purpose, the dimensions of the dental surfaceare first determined and are then positioned on a stored toothreplacement or in the region of a three-dimensional virtual preparationsite. At the same time, the position of the digital dental surface inthe tooth replacement or in the preparation site can be determined in atleast one direction in space and/or one direction of rotation.

In one embodiment, a dental surface of the contralateral tooth is usedas a mirror image in order to form the surface of the restoration. Inthe process, the selected dental surface is mirrored using mirrorimaging means, whereby a selection dialog is displayed. The size of theselected dental surface can also be changed, such that the surface canbe adapted to the adjacent teeth. Using alignment tools, the position ofthe selected dental surface can be changed horizontally, vertically,with respect to the tilt and with respect to the enlargement. Theselected dental surface is transferred using the conventional CADmachining tools. After adapting the selected dental surface of the toothcontralateral to the tooth to be fabricated, the surface created isgraphically amalgamated with the preparation, whereby the toothreplacement to be fabricated is formed.

One disadvantage of this process is that the selection, the transfer andthe adaptation of the dental surface of the contralateral tooth,although virtual, are nevertheless expensive and time-consuming for theuser.

Another disadvantage is that in the manual adaptation of the selecteddental surface by mirroring, altering the alignment, the extension andthe tilt, the tooth replacement can be deformed, such that the estheticdemand on the symmetry of the tooth to be fabricated with thecontralateral tooth is not met.

Another disadvantage is that, for the creation of a restoration wherethere are multiple teeth to be replaced, all the steps mentioned for theentire method are to be performed for each individual tooth.

Hence, the object of this invention is to make available a device or amethod for the symmetrical editing of a virtual 3-D model, which enablestime-saving editing and guarantees a symmetry of the teeth to befabricated with their contralateral teeth.

DESCRIPTION OF THE INVENTION

This object is achieved by means of the present invention.

In accordance with the invention, a device is provided for editing avirtual 3-D model of teeth positioned in a dental arch by means of avirtual tool. The tool can be used on a first tooth of the model,whereby the corresponding application is applied to a second toothmirrored to the first contralateral tooth with respect to a plane ofsymmetry, that is to the tooth on the other side of the plane ofsymmetry, which is positioned in respect of the plane of symmetry as amirror image of the first tooth.

The device according to the invention can be a computer system withoperating controls, such as a keyboard and mouse, which is suitable forediting the virtual 3-D model of teeth. Thereby, the virtual 3-D modelcan be adapted by means of CAD software to a three-dimensional data setfor a preparation site, which has been measured with an intraoralcamera. The computer system may also feature a display unit.

The 3-D model of the dental arch can display at least two symmetricalteeth to be replaced, such as the incisors 12, 11, 21, 22 of the maxillaor 42, 41, 31, 32 of the mandible, in accordance with the FDI diagram.The 3-D model may also display a divergent number of teeth to bereplaced on the left and right side, for example the teeth 13, 12, 11 onthe right side of the maxilla and the adjacent teeth 21, 22 on the leftside of the maxilla. Thereby, the application can be applied to theteeth 12, 11 mirrored by the teeth 21, 22 along the plane of symmetry.

The user can perform various editing steps by means of the virtual tool,such as rotation, enlarging, altering the position, reducing andaltering the shape.

The application using the tool on a first tooth is mirrored across theplane of symmetry and is correspondingly carried out on the second toothpositioned symmetrically to the first tooth, such that this is alsoedited symmetrically to the first tooth.

The predefined virtual 3-D model is, as a rule, symmetrical, such thatthe plane of symmetry is positioned between the teeth 11 and 21 in themaxilla or between the teeth 41 and 31 in the mandible in accordancewith the FDI diagram.

This symmetrical virtual 3-D model can be adjusted to the individualsituation in the patient's oral cavity, by, for example, displacing thedivergent part of the SD model using an offset and superimposing theactual course of the jaw in the patient's oral cavity from a visualthree-dimensional image of the dental situation.

Alternately, in a first step, a draft of the application symmetricalalong the set plane of symmetry can be created. In the second step, thisdraft can be shifted around an offset in order to adjust the symmetricaldraft to the actual course of the jaw.

The plane of symmetry can also be manually set by the user.

The plane of symmetry can also be determined by means of a computer, bysuperimposing the mirror image of the right-hand section of the dentalarch along the plane of symmetry onto the left-hand section of thedental arch.

One advantage of this device is that the second tooth is automaticallyadapted to the first contralaterally positioned tooth by the computer.Thus, the symmetry of the virtual 3-D model in respect of the plane ofsymmetry is guaranteed in the editing of one side with respect to theother side. The user must only edit one side using the virtual tool. Theteeth contralaterally positioned on the other side of the plane ofsymmetry are automatically adapted by the computer, such that the lengthof time for the creation of the virtual 3-D model is shortened.

Advantageously, using a computer, the mirrored application of the toolon the contralateral tooth can be performed simultaneously with theapplication on the first tooth.

Thus, the parameters of the application of the tool on the first toothdo not have to be saved in order to perform the mirrored application ofthe tool on the contralateral tooth at a later point in time. Themirrored application on the contralateral tooth takes placesimultaneously without delay, by converting the parameters of theapplication on the first tooth in compliance with the mirror image of aplane of symmetry and applying these to the contralateral tooth.

Advantageously, the tool can effect a rotation of the first tooth arounda first axis of rotation and a corresponding mirrored rotation of thesecond contralateral tooth around a second mirrored axis of rotation.

Thus, the rotation of the first tooth relative to the plane of symmetryis mirrored and applied to the second contralateral tooth. Theindividual rotation parameters, such as the angle of the axis ofrotation to the dental arch, the direction of rotation and the angle ofrotation, are applied to the second contralateral toothmirror-symmetrically with respect to the plane of symmetry.

Advantageously, the tool can effect an enlargement or a reduction of thefirst tooth and of the second contralateral tooth by a scale factor.

Thus, the size of the virtual tooth can be adjusted in order to adapt itto the dental arch. The change in size is simultaneously applied to thesecond contralateral tooth such that the adjustment to the size is mademirror-symmetrically.

Advantageously, the tool can effect a change in the position with thesame alignment of the first tooth and a change in the position of thesecond contralateral tooth mirrored around the sectional planes.

Thus, the tooth can be shifted relative to the dental arch, whereby thealignment of the tooth remains the same, such that the tooth can beadjusted to the adjacent teeth and the second contralateral tooth can becorrespondingly shifted in a mirrored direction.

Advantageously, the tool can effect a change in the shape of the surfaceof the first tooth and accordingly, effect a mirrored change in theshape of the surface of the second contralateral tooth.

Thus, the surface of the tooth can be virtually modified. For example,so-called freeform tools can be used in order to insert hollows, ridgesand small grooves or fissures into the surface of the virtual tooth.These dentally esthetic changes in the surface are then correspondinglymirrored on the contralateral tooth, without the user's intervention, bycomputer.

Advantageously, the changes made by the application of the tool on thefirst tooth and on the second contralateral tooth can be displayed.

Thus, the changes are visible to the user on a display device, such as amonitor, and hence can be tracked.

The changes can also be undone. The mirrored changes to thecontralateral tooth during editing using the tool are also displayed.

Advantageously, the plane of symmetry can be set by the user.

For example, the plane of symmetry can be virtually shifted and turnedby the user in order to position the plane of symmetry between teeth 11and 21 in the maxilla or between teeth 41 and 31 in the mandible, inaccordance with the FDI diagram. Thereby, the plane of symmetry ispositioned such that the mirror image of a left-hand section of thedental arch along the plane of symmetry is superimposed on theright-hand section of the dental arch.

Advantageously, the plane of symmetry can be determined by computer byreference to the course of the dental arch and/or by reference to thepositioning and shape of adjacent teeth in the 3-D model of the teeth tobe replaced and/or by reference to the positioning and shape ofantagonists to the teeth of the 3-D model.

Thus, the plane of symmetry is automatically defined by means of thecomputer. In doing so, a computer algorithm can be used, which mirrorsone section of the dental arch on any selected level and compares thissection with the opposing section of the dental arch. The plane ofsymmetry is determined where there are consistencies in the mirror imagewith the opposing section.

One further object of the invention is a corresponding method forediting a virtual 3-D model of the teeth positioned in a dental arch bymeans of a virtual tool. The tool is applied to a first tooth of themodel, whereby the corresponding application is carried out on a secondtooth, mirrored to the first contralateral tooth with reference to aplane of symmetry, that is, on the tooth on the other side of the planeof symmetry, which is located in a mirrored position relative to thefirst tooth with reference to the plane of symmetry.

At the same time, symmetrical operators in the CAD area can be used. Oneadvantage of the method according to the invention is that the timespent editing is reduced since the changes must only be made in onesection of the dental arch, and these are automatically mirrored in thesecond section of the dental arch. A further advantage is that a perfectsymmetry of both sections is produced and hence the dental esthetics areguaranteed.

Advantageously, the mirrored application of the tool on thecontralateral tooth can be performed simultaneously by computer forapplication on the first tooth.

The simultaneous application on the contralateral tooth has theadvantage that the changes do not have to be stored and are applieddirectly by computer, mirrored on the contralateral tooth.

Advantageously, the tool can effect a rotation of the first tooth and acorresponding mirrored rotation of the second contralateral tooth aroundan axis of rotation.

Using the tool, the rotation can be effected virtually by means of arotation operator, whereby the rotation operator is applied to thecontralateral tooth as a mirror image on the plane of symmetry.

Advantageously, the tool can effect an enlargement or a reduction of thefirst and of the second contralateral tooth by a scale factor.

The enlargement or the reduction can be effected by means of anenlargement operator on the first tooth, whereby this enlargementoperator can simultaneously alter the size of the second contralateraltooth.

Advantageously, the tool can effect a change in the position with thesame orientation of the first tooth and a mirrored change in theposition of the second contralateral tooth around the plane of symmetry.

The process step of changing the position of the first tooth can beeffected by means of a displacement operator, whereby this is applied asa mirror image of the second contralateral tooth.

Advantageously, the tool can effect a change in the shape of the surfaceof the first tooth and effect an analogous mirrored change in the shapeof the surface of the second contralateral tooth.

For the esthetic matching of the surface of the first tooth, so-calledfreeform tools can be used in order to shape hollows, ridges andfissures. These changes are simultaneously carried outmirror-symmetrically on the second contralateral tooth.

Advantageously, the changes in the application of the tool on the firsttooth and on the second contralateral tooth can be displayed.

Thanks to the display of the changes, the user can better track thesechanges. The changes can also be undone.

Advantageously, the plane of symmetry can be set by the user.

Using displacement operators and rotation operators, the user can changethe virtual position of the plane of symmetry relative to the dentalarch. A mirror image of one section of the dental arch can be displayedon the plane of symmetry as an aid for the user. Thus, the user can moreeasily determine where the plane of symmetry is positioned by trying tocorrelate the mirror image of a section of the dental arch with theopposing section of the dental arch.

Advantageously, the plane of symmetry can be determined by computer, byreference to the course of the dental arch and/or by reference to thepositioning and shape of adjacent teeth of the 3-D model of the teeth tobe replaced and/or by reference to the positioning and shape ofantagonists of the teeth of the 3-D model.

Thus, the plane of symmetry is automatically determined by computer. Theadvantage is that, as a result, the time spent planning the virtual 3-Dmodel is reduced using the method in accordance with the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings depict examples of the realization of the invention. Thedrawings depict:

FIG. 1 Sketch of one embodiment of the device according to theinvention, consisting of a computer, a monitor, a keyboard, a mouse andan intraoral camera;

FIG. 2 Sketch of a virtual 3-D model of teeth positioned in a dentalarch;

FIG. 3 Sketch of the application of a virtual shifting tool;

FIG. 4 Sketch of the depiction of the identification of the plane ofsymmetry.

EXAMPLES

FIG. 1 depicts an embodiment of the device 1 in accordance with theinvention for symmetrical editing of a virtual 3-D model 2 of teeth 2.1,2.2, 2.3 and 2.4 positioned in a dental arch by means of a virtual tool3. The device 1 is realized as a computer, which is connected to amonitor 4, a keyboard 5, a mouse 6 and an intraoral camera 7 forrecording visual three-dimensional images. The 3-D model 2 of therestoration, consisting of the teeth to be replaced 2.1, 2.2, 2.3 and2.4, which are positioned between the teeth of a three-dimensional image8 of a mandible 9 of a patient 10, whereby the visual image 8 comprisesthe teeth 8.1 to 8.6, which correspond to teeth 43, 44, 45 and 33, 34,35 of the mandible in accordance with the FDI dental diagram. The teeth2.1 to 2.4 to be replaced in the planned restoration correspond to theteeth 41, 42, 31 and 32 in accordance with the FDI dental diagram.Correspondingly, the visual imaging and the planning for a restorationcan also be carried out for the patient's 10 maxilla 11. A virtual planeof symmetry 12 is depicted between the teeth 2.1 and 2.2, which ispositioned vertically to the viewing level of the monitor 4 and hence isdepicted as a line. The teeth 2.2, 2.4 are positioned contralaterally tothe teeth 2.1 and 2.3.

FIG. 2 depicts a sketch of the virtual 3-D model 2, consisting of thevirtual teeth 2.1 to 2.4, which are positioned between the adjacentteeth 8.1 and 8.2 of the three-dimensional image 8 of the mandible 9.The plane of symmetry 12, which is vertical to the plane displayed andhence is depicted as a line, is positioned between the teeth 2.1 and2.2. Several virtual tools are arranged in a drop-down menu 20, namely afirst tool 21 for enlargement by a scale factor, a second tool 22 forreduction by a scale factor, a third tool 23 for changing the positionin a vertical direction with the same alignment, a fourth tool 24 forchanging the position in a horizontal direction, a fifth tool 25 forrotating a tooth around an axis in a clockwise direction, a sixth tool26 for rotating a tooth around an axis in a counterclockwise direction,a seventh tool 27 for changing the shape of a surface, whereby aselected region is elevated, and an eighth tool 28 for editing the shapeof a surface, whereby a selected region is lowered relative to thedental surface.

These tools are used for editing the virtual model 2. Multiple editingsteps are depicted in FIG. 2. In the first editing step, the tool 21 wasselected from the drop-down menu 20 and applied to the tooth 2.3 by theuser using the operating controls 5 and 6 in FIG. 1, whereby an originalmodel 29 of a tooth from a dental database, represented by a dashedline, was consistently enlarged by a particular scale factor. Theenlargement is represented by the arrows 30. The tool 21 is representedby a first cursor. The user can, for example, select the original 3-Dmodel 29 of the tooth from a dental database using the cursor andenlarge the 3-D model 29 to the desired size of the planned tooth 2.3 bymoving the cursor away from the 3-D model. An enlargement operator ofthe software used is then used simultaneously on the contralateral tooth2.4 and simultaneously effects a corresponding enlargement of a model 31of a contralateral tooth, which depicts a mirror image of the originaltooth 29 relative to the plane of symmetry 12. The enlargement of themirrored tooth 31 is depicted by the arrows 32. Hence, the applicationof the tool 21 effects an enlargement of the tooth 2.3 and asimultaneous enlargement of the contralateral mirrored tooth 2.4 by thesame scale factor.

In a second step of the process, the tool 26 for rotation around aselected axis is used on the tooth 2.1, whereby the tool 26 is depictedby a second cursor. Thereby, the user can set an axis of rotation 33 inorder to turn the tooth 2.1 from an initial position 34, represented bya dashed line, by rotation in a counterclockwise direction around theselected axis 33 into the end position 35, represented by a solid line.The application of the tool 26 on the tooth 2.1 also effects a mirroredrotation of the contralateral tooth 2.2 around an axis of rotation 36,mirrored across from the plane of symmetry 12, in a clockwise direction,as represented by the arrow 37, whereby the tooth 2.2 is moved from aninitial position 38, represented by a dashed line, into an end position39. Hence, the application of the tool 26 effects both the rotation ofthe tooth 2.1 and the mirrored rotation of the contralateral tooth 2.2.

In a third step, the tool 28 is applied to a labial surface 40 of thetooth 2.1, whereby a selected region 41, represented by the dashed line,is lowered relative to the labial surface 40. The tool 28 is representedby a third cursor. In applying the tool 28 to the tooth 2.1, a region 42of the contralateral tooth 2.2 mirrored relative to the plane ofsymmetry 12 is simultaneously lowered on the contralateral tooth 2.2relative to the labial surface 43 of the tooth 2.2 by the same height asthe selected region 41. The tool 28 is a so-called freeform tool andthis effects the change in the surface 40 of the tooth 2.1 and,simultaneously, a mirrored change in the surface 43 of the contralateraltooth 2.2.

In a further step, hollows (fissures) are incorporated into the occlusalsurface 45 of the tooth 2.3 by means of another freeform tool 44.Simultaneously with the change to the occlusal surface 45, an occlusalsurface 46 of the contralateral tooth 2.4 is correspondinglymirror-symmetrically changed by incorporating the mirrored hollows intothe occlusal surface 46. Hence, the application of the tool 44 effects achange in the occlusal surface 45 of the tooth 2.3 and a simultaneousmirrored change in the occlusal surface 46 of the contralateral tooth2.4.

In FIG. 3, the application of the tools 24 for changing the position ofthe tooth with the same orientation is represented, whereby the tool isindicated by a cursor 50. By means of the cursor 50, the user can shiftthe tooth 2.1 from an initial position 51, represented by a dashed line,to an end position 52, represented by a solid line, whereby theorientation of the tooth remains unchanged. In applying the tool 2.1 forchanging the position by means of the cursor 50 to the tooth, thecontralateral tooth 2.2 mirrored relative to the plane of symmetry 12 issimultaneously shifted from an initial position 53 to an end position54. The displacement of the tooth 2.1 is represented by the arrows 55and that of the tooth 2.2 by the arrows 56.

In FIG. 4, a step of the process is represented, in which the plane ofsymmetry 12 is determined by the user. In order to facilitate locatingthe plane of symmetry, the left side of the dental arch 60, consistingof the teeth 2.1 and 2.3 to be replaced and the teeth 8.1 and 8.2 in thevisual three-dimensional image 8 in FIG. 1, is mirrored on the axis ofsymmetry 12.1 in an initial position. The mirror image 61 of the leftsection 60 of the dental arch is represented by a dashed line. Based onthe initial position 12.1, the plane of symmetry 12 is turned andshifted until it reaches an end position 12.2, in which the mirror image61 of the left section 60 of the dental arch coincides as much aspossible with the right section 62. The right section 62 is representedas a solid line and consists of the teeth 2.2 and 2.4 of the 3-D model 2to be replaced, together with the teeth 8.2 and 8.4 in thethree-dimensional visual image 8 in FIG. 1. The rotation of the plane ofsymmetry 12 is represented by the arrow 63 and is operated by means of avirtual tool 64, to change the position of the plane of symmetry. Theplane of symmetry 12 can also be determined by computer, whereby theposition of the plane of symmetry 12 is changed by means of a computeralgorithm until the mirror image 61 of the left section 60 of the dentalarch coincides as much as possible with the right section 62 of thedental arch. Image data for the positioning and the shape of the dentalarch and of adjacent teeth and antagonists can also be taken intoaccount in the computer-aided determination of the plane of symmetry.

LIST OF REFERENCE SYMBOLS

-   -   1 Device    -   2 3-D model    -   2.1-2.4 Teeth of the 3-D model    -   3 Tool    -   4 Screen    -   5 Keyboard    -   6 Mouse    -   7 Intraoral camera    -   8 Image    -   8.1-8.6 Teeth in the image    -   9 Mandible    -   10 Patient    -   11 Maxilla    -   12 Plane of symmetry    -   12.1 Initial position of the axis of symmetry    -   12.2 End position of the axis of symmetry    -   20 Drop-down menu    -   21 First tool    -   22 Second tool    -   23 Third tool    -   24 Fourth tool    -   25 Fifth tool    -   26 Sixth tool    -   27 Seventh tool    -   28 Eighth tool    -   29 Original model of a tooth    -   30 Arrow    -   31 Mirror image of the model 29    -   32 Arrow    -   33 Axis of rotation    -   34 Initial position of the tooth    -   35 End position of the tooth    -   36 Mirrored axis of rotation    -   37 Direction arrow    -   38 Initial position    -   39 End position    -   40 Labial surface    -   41 Selected region    -   42 Mirrored region    -   43 Labial surface    -   44 Freeform tool    -   45 Occlusal surface    -   46 Occlusal surface    -   50 Cursor    -   51 Initial position    -   52 End position    -   53 Initial position    -   54 End position    -   55 Arrow    -   56 Arrow    -   60 Left section    -   61 Mirror image/Dental arch    -   62 Right section    -   63 Arrow    -   64 Tool

The invention claimed is:
 1. An apparatus, comprising: a computerconfigured to: perform an edit of a first tooth in a three-dimensionalmodel of teeth positioned in a dental arch; and perform, in response tothe edit of the first tooth in the three-dimensional model, an edit of asecond tooth in the three-dimensional model that corresponds to the editof the first tooth, wherein the second tooth is contralateral to thefirst tooth with respect to a plane of symmetry, and is positioned as amirror image of the first tooth with respect to the plane of symmetry,wherein the three-dimensional model of teeth is based onthree-dimensional images of a patient's teeth generated by an intraoralcamera, and wherein the edit of the second tooth is performedsimultaneously with the edit of the first tooth.
 2. The apparatus ofclaim 1, wherein the edit of the first tooth effects a rotation of thefirst tooth around a first axis of rotation and the edit of the secondtooth effects a corresponding mirrored rotation of the second tootharound a second axis of rotation.
 3. The apparatus of claim 1, whereinthe edit of the first tooth effects an enlargement or a reduction of thefirst tooth by a scale factor and the edit of the second tooth effectsan enlargement or a reduction of the second tooth by the scale factor.4. The apparatus of claim 1, wherein the edit of the first tooth effectsa change in a position of the first tooth with a same orientation andthe edit of the second tooth effects a mirrored change in a position ofthe second tooth around the plane of symmetry.
 5. The apparatus of claim1, wherein the edit of the first tooth effects a change in a shape of asurface of the first tooth and the edit of the second tooth effects acorresponding mirrored change in a shape of a surface of the secondtooth.
 6. The apparatus of claim 1, further comprising: a displaydevice, wherein the computer is further configured to display an editedfirst tooth and an edited second tooth on the display device.
 7. Theapparatus of claim 1, wherein the computer is further configured toreceive an instruction representing the plane of symmetry.
 8. Theapparatus of claim 1, wherein the computer is further configured todetermine the plane of symmetry by reference to one or more of: (i) acourse of the dental arch, (ii) a position and a shape of a toothadjacent to the first tooth in the three-dimensional model, and (iii)positions and shapes of antagonists to the teeth in thethree-dimensional model.
 9. A method of editing a dental model,comprising: editing, using a computer, a first tooth in athree-dimensional model of teeth positioned in a dental arch; editing,using the computer and in response to the editing of the first tooth inthe three-dimensional model, a second tooth in the three-dimensionalmodel in a corresponding manner to the first tooth, wherein the secondtooth is contralateral to the first tooth with respect to a plane ofsymmetry and is positioned as a mirror image of the first tooth withrespect to the plane of symmetry, wherein the three-dimensional model ofteeth is based on three-dimensional images of a patient's teethgenerated by an intraoral camera, and wherein the editing of the secondtooth is performed simultaneously with the editing of the first tooth.10. The method in accordance with claim 9, wherein the editing of thefirst tooth effects a rotation of the first tooth around a first axis ofrotation and the editing of the second tooth effects a correspondingmirrored rotation of the second tooth around a second axis of rotation.11. The method in accordance with claim 9, wherein the editing of thefirst tooth effects an enlargement or a reduction of the first tooth bya scale factor and the editing of the second tooth effects anenlargement or a reduction of the second tooth by the scale factor. 12.The method in accordance with claim 9, wherein the editing of the firsttooth effects a change in a position of the first tooth with a sameorientation and the editing of the second tooth effects a mirroredchange in a position of the second tooth around the plane of symmetry.13. The method in accordance with claim 9, wherein the editing of thefirst tooth effects a change in a shape of a surface of the first toothand the editing of the second tooth effects a corresponding mirroredchange in a shape of a surface of the second tooth.
 14. The method inaccordance with claim 9, further comprising: displaying an edited firsttooth and an edited second tooth on a display device.
 15. The method inaccordance with claim 9, further comprising: receiving an instructionrepresenting the plane of symmetry.
 16. The method in accordance withclaim 9, further comprising: determining, using the computer, the planeof symmetry based on one or more of: (i) a course of the dental arch(ii) a position and a shape of a tooth adjacent to the first tooth inthe three-dimensional model, and (iii) positions and shapes ofantagonists to the teeth in the three-dimensional model.